The mathematical technology of the decision of linear and nonlinear regional problems is stated. On the basis of methods quasi-linearization, operational calculation and splitting on spatial variables the exact and approached analytical decisions of the equations in private derivatives of the first and second order are received. Conditions of unequivocal resolvability of a nonlinear regional problem are found and the estimation of speed of convergence of iterative process is given. On an example of trial functions results of comparison of the analytical decisions received on offered mathematical technology, with the exact decision of regional problems and with numerical decisions on known methods are resulted. For science officers and students of older years of physical and mathematical specialists.